Quantization-based Optimization with Perspective of Quantum Mechanics
This work addresses a foundational problem in optimization theory by bridging quantum mechanics concepts to global optimization, though it appears incremental as it builds on existing quantum-inspired methods.
The paper tackled the need for a new analysis framework for global optimization algorithms by providing an analysis based on the Schrödinger equation to reveal how quantum mechanics properties enable global optimization, confirming that the tunneling effect allows escape from local minima and validating this with experiments on standard multi-modal benchmark functions.
Statistical and stochastic analysis based on thermodynamics has been the main analysis framework for stochastic global optimization. Recently, appearing quantum annealing or quantum tunneling algorithm for global optimization, we require a new researching framework for global optimization algorithms. In this paper, we provide the analysis for quantization-based optimization based on the Schrödinger equation to reveal what property in quantum mechanics enables global optimization. We present that the tunneling effect derived by the Schrödinger equation in quantization-based optimization enables to escape of a local minimum. Additionally, we confirm that this tunneling effect is the same property included in quantum mechanics-based global optimization. Experiments with standard multi-modal benchmark functions represent that the proposed analysis is valid.